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Design and Discovery of New Piezoelectric Materials Using Density Functional Theory

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Design and Discovery of New Piezoelectric Materials Using Density Functional Theory DESIGN AND DISCOVERY OF NEW PIEZOELECTRIC MATERIALS USING DENSITY FUNCTIONAL THEORY by Sukriti Manna © Copyright by Sukriti Manna, 2018 All Rights Reserved A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering). Golden, Colorado Date Signed: Sukriti Manna Signed: Dr. Cristian V. Ciobanu Thesis Advisor Signed: Dr. Vladan Stevanovi´c Thesis Advisor Golden, Colorado Date Signed: Dr. John Berger Professor and Head Department of Mechanical Engineering ii ABSTRACT Piezoelectric materials find applications in microelectromechanical systems (MEMS), such as surface acoustic wave (SAW) resonators, radio frequency (RF) filters, resonators, and energy harvesters. Using density functional theory calculations, the present study illus- trates the influence of alloying and co-alloying with different nitrides on piezoelectric and mechanical properties of an existing piezoelectric material such as aluminum nitride (AlN). Besides improving the performance of existing piezoelectric material, a high-throughput screening method is used to discover new piezoelectric materials. AlN has several beneficial properties such as high temperature stability, low dielectric permittivity, high hardness, large stiffness constant, high sound velocity, and complementary metal-oxide-semiconductor (CMOS) compatibility. This makes it widely accepted material in RF and resonant devices. However, it remains a challenge to enhance the piezoelectric modulus of AlN. The first part of this thesis establishes that the piezoelectric modulus of AlN could be improved by alloying with rocksalt transition metal nitrides such as scandium nitride (ScN), yttrium nitride (YN), and chromium nitride (CrN). As the content of the rocksalt end member in the alloy increases, the accompanying structural frustration enables a greater piezoelectric response. This structural frustration is also accompanied by thermodynamic driving forces for phase separation which, with increased alloy concentration, lead to the destruction of the piezoelectric response upon transition to the (centrosymmetric, cubic) rocksalt structure. Thus, it becomes necessary to identify suitable alloying elements that may yield highest piezoelectric response with minimal alloying additions. The study reveals that the alloying with CrN would lead to the lowest transition composition (occurring at approximately 25% CrN concentration) between the wurtzite and rocksalt structures, thereby allowing piezoelectric enhancements at alloying levels that are easier to stabilize during the synthesis. The present study indicates that, for 25% CrN alloying, the piezoelectric modulus iii is about 4 times larger than that of pure AlN. Thus, it is proposed to use CrxAl1−xN as a suitable replacement for AlN. One of the adverse effect of transition metal nitride alloying for improvement of piezoelec- tric response is accompanied by the softening of AlN lattice. This would make the material less desirable for resonant applications. Our subsequent research establishes that co-alloying with YN and BN would enable the most superior combination of piezoelectric and mechanical properties of AlN. The rest of the thesis describes our efforts for identifying new piezoelectric materials. This requires high-throughput screening of inorganic materials for their piezoelectric properties. Our quest to search for new piezoelectric compounds is motivated by the notion that soft materials have the opportunity to exhibit large piezoelectric response (piezoelectric modulus d), and the knowledge that the van der Waals (vdW) layered materials are typically soft in the layer stacking direction. From a pool of 869 vdW structures, we have discovered 50 new compounds such as In2Te5, GeTe, and CuVO3 having piezoelectric response larger than AlN. Remarkably, 70% of our discovered piezoelectric candidates do not contain any toxic elements like Pb. Our analysis reveals that the large components of d always couple with the deformations (shearing or axial) of van der Waals “gaps” between the layers. This research establishes a wide scope of synthesizing vdW materials for applications demanding high piezoelectric modulus. iv TABLE OF CONTENTS ABSTRACT ......................................... iii LISTOFFIGURES ..................................... ix LISTOFTABLES ..................................... xiii LISTOFSYMBOLS.....................................xiv LISTOFABBREVIATIONS ................................ xv ACKNOWLEDGMENTS ................................. xvii DEDICATION ........................................xix CHAPTER1 INTRODUCTION ...............................1 1.1 PiezoelectricEffectandApplications . ........2 1.2 Classification of Piezoelectric Materials . ............3 1.3 Vector/Tensor Quantities Related to Piezoelectricity ...............4 1.4 ConstitutiveEquations . .....5 1.5 FiguresofMeritofPiezoelectricDevices . .........7 1.5.1 FiguresofMerit................................7 1.5.2 PiezoelectricDevices . ...9 1.6 Piezoelectric Materials: Present Status and Motivation for Computational Investigations .................................... 14 1.6.1 MaterialsbasedonSingleCrystal . .... 15 1.6.2 Materials Based on Polycrystalline Materials . .........18 1.6.3 Toxicity of Lead-based Piezoelectrics . ....... 23 v 1.6.4 Motivation for Computational Research on Improving Piezoelectric Materials ..................................23 1.6.5 Prior Computational Studies of Piezoelectric Properties......... 25 1.7 Objectives...................................... 26 1.7.1 Improving Performance of Existing Piezoelectric Materials . 27 1.7.2 Searching for New Piezoelectric Materials. ....... 27 1.8 OrganizationoftheThesis . .... 28 CHAPTER 2 ENHANCED PIEZOELECTRIC RESPONSE OF AlN via CrN ALLOYING .................................31 2.1 Introduction.................................... 32 2.2 Methods.......................................34 2.2.1 Paramagnetic Representation of Cr-AlN Alloys. ...... 34 2.2.2 DetailsoftheDFTCalculations . 34 2.2.3 ExperimentalProcedures. 36 2.3 ResultsandDiscussion . 36 2.3.1 EnthalpyofMixing............................. 36 2.3.2 PiezoelectricStressCoefficients . ..... 37 2.3.3 Comparison with Other Wurtzite-Based Alloys . ...... 42 2.3.4 ExperimentalResults. 46 2.4 ConcludingRemarks ............................... 48 CHAPTER 3 TUNING THE PIEZOELECTRIC AND MECHANICAL PROPERTIES OF THE AlN SYSTEM VIA ALLOYING WITH YN ANDBN ...................................52 3.1 Introduction.................................... 52 3.2 Methods.......................................55 vi 3.3 ResultsandDiscussions . 57 3.4 Conclusion...................................... 64 CHAPTER 4 LARGE PIEZOELECTRIC RESPONSE OF VAN DER WAALS LAYEREDSOLIDS ............................. 66 4.1 Introduction.................................... 66 4.2 ComputationalMethodology. .... 70 4.2.1 Automated Identification of Quasi-2D Materials . ....... 70 4.2.2 Calculating Piezoelectric Properties of Quasi-2D Materials . 71 4.2.3 Workflow for identifying quasi-2D piezoelectrics . ..........74 4.3 ResultsandDiscussions . 75 4.3.1 Promising Quasi-2D Piezoelectric Materials . ........75 4.3.2 RoleofvanderWaalsInteractions . 80 4.3.3 Axial Piezoelectric and Elastic Anisotropy . ...... 82 4.4 Conclusions ..................................... 84 CHAPTER 5 SUMMARY & CONCLUSIONS . 86 5.1 Conclusions ..................................... 86 5.2 RecommendationsforFutureWork . .... 87 REFERENCESCITED ................................... 88 APPENDIX A CLASSIFICATION OF PIEZOELECTRIC MATERIALS . 110 APPENDIX B DENSITY FUNCTIONAL THEORY METHODS . 112 B.1 Many-bodySchr¨odingerequation . .... 112 B.2 DensityFunctionalTheory . 113 B.2.1 Hohenberg-KohnTheorem . 113 vii B.2.2 TheKohn-ShamEquations . 114 B.2.3 LocalDensityApproximation . 115 B.2.4 GeneralizedGradientApproximation . 116 B.3 Technicalimplementation . 116 APPENDIXC SIMULATINGELASTICPROPERTIES . 117 APPENDIX D MODELING OF RANDOM ALLOYS . 118 D.1 DetailsforGeneratingSQSStructures . ...... 118 D.2 Dispersion of e33 and C33 values for different Y concentration . 119 APPENDIX E ADDITIONAL SUPPLEMENTARY INFORMATION OF CHAPTER3 ............................... 121 E.1 Variations of e31 and C11 withYandBcomposition . 121 E.2 Piezoelectric moduli as functions of composition . ........... 121 APPENDIX F SUPPLEMENTARY INFORMATION OF CHAPTER 4 . 124 F.1 Comparison of Experimental and Calculated PiezoelectricModulus . 124 F.2 Axial Anisotropies: C vs e ............................ 125 F.3 Experimentally Measured Elastic Constants of Quasi-2D Materials. 125 F.4 Schematics of Different Modes of d ....................... 126 F.5 Rotation of d, e, and C -matrices ........................ 127 APPENDIX G PERMISSIONS FOR CONTENT REUSED . 129 viii LIST OF FIGURES Figure 1.1 Schematics of direct piezoelectric effects: (a) at applied compressive stress, (b) at applied tension. (c) and (d) describe the schematics of converse piezoelectric effect at applied electric field. ..........3 Figure 1.2 Classification of piezoelectric materials. They are classified into of piezoelectric, pyroelectric, and ferroelectric materials. ............4 Figure1.3 CorrelationbetweendifferentFOMs . ........13 Figure 1.4 The advancement and milestones of piezoelectric singlecrystals . 15 Figure 1.5 α-Quartz used as a piezoelectric oscillator in a watch . ..... 17 Figure 2.1 Schematics of cation sublattice of CrxAl1−xN alloy. Al (Cr) sites are shown as gray
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